We introduce a general framework for generating diverse visual content,
including ambiguous images, panorama images, mesh textures, and Gaussian splat
textures, by synchronizing multiple diffusion processes. We present exhaustive
investigation into all possible scenarios for synchronizing multiple diffusion
processes through a canonical space and analyze their characteristics across
applications. In doing so, we reveal a previously unexplored case: averaging
the outputs of Tweedie's formula while conducting denoising in multiple
instance spaces. This case also provides the best quality with the widest
applicability to downstream tasks. We name this case SyncTweedies. In our
experiments generating visual content aforementioned, we demonstrate the
superior quality of generation by SyncTweedies compared to other
synchronization methods, optimization-based and iterative-update-based methods.

通过同步多个扩散过程，我们引入了一个生成多样化视觉内容（包括模糊图像、全景图像、网格纹理和高斯斑点纹理）的通用框架，并通过一个标准空间对同步多个扩散过程的所有可能情况进行了详尽研究，并分析了它们在各种应用中的特点。在此过程中，我们揭示了一个以往未曾探索的情况：在多实例空间中进行去噪并对 Tweedie's 公式的输出取平均。这种情况提供了与下游任务的最广泛适用性相比最好的质量。我们将这种情况命名为 SyncTweedies。在我们生成上述视觉内容的实验中，我们证明了 SyncTweedies 相对于其他同步方法（基于优化和基于迭代更新的方法）的生成质量更高。

SyncTweedies: 基于同步扩散的通用生成框架

SyncTweedies: A General Generative Framework Based on Synchronized  Diffusions

Likelihood-based deep generative models have recently been shown to exhibit
pathological behaviour under the manifold hypothesis as a consequence of using
high-dimensional densities to model data with low-dimensional structure. In
this paper we propose two methodologies aimed at addressing this problem. Both
are based on adding Gaussian noise to the data to remove the dimensionality
mismatch during training, and both provide a denoising mechanism whose goal is
to sample from the model as though no noise had been added to the data. Our
first approach is based on Tweedie's formula, and the second on models which
take the variance of added noise as a conditional input. We show that
surprisingly, while well motivated, these approaches only sporadically improve
performance over not adding noise, and that other methods of addressing the
dimensionality mismatch are more empirically adequate.

本文提出使用高斯噪声来解决高维密度函数模拟低维结构数据时的维度不匹配问题，并基于 Tweedie's 公式和噪声方差为条件的模型提出了两种方法。研究结果表明，虽然这些方法在理论上有合理性，但在实践中表现不一，并不是解决维度不匹配问题的最佳方案。

去噪深层生成模型

Denoising Deep Generative Models

The first order derivative of a data density can be estimated efficiently by
denoising score matching, and has become an important component in many
applications, such as image generation and audio synthesis. Higher order
derivatives provide additional local information about the data distribution
and enable new applications. Although they can be estimated via automatic
differentiation of a learned density model, this can amplify estimation errors
and is expensive in high dimensional settings. To overcome these limitations,
we propose a method to directly estimate high order derivatives (scores) of a
data density from samples. We first show that denoising score matching can be
interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's
formula on higher order moments, we generalize denoising score matching to
estimate higher order derivatives. We demonstrate empirically that models
trained with the proposed method can approximate second order derivatives more
efficiently and accurately than via automatic differentiation. We show that our
models can be used to quantify uncertainty in denoising and to improve the
mixing speed of Langevin dynamics via Ozaki discretization for sampling
synthetic data and natural images.

提出了一种直接从样本估计高阶导数的方法，并将其应用于数据密度的分析与合成，提高了模型的精度和效率。